Answer:
The slope (m) and y-intercept (b), so the equation of the line in slope-intercept form is:
[tex]y = \frac{13}{3}x - \frac{7}{3}[/tex].
Step-by-step explanation:
To express the equation of a line in slope-intercept form (y = mx + b), where mm is the slope and b is the y-intercept, you need to find the values of m and b using the given points [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex].
Let's use the points (1, 2) and (-2, -11).
1. Calculate the slope (m):
[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
[tex]m = \frac{(-11)-2}{(-2)-1} = \frac{-13}{-3}[/tex]
[tex]m = \frac{13}{3}[/tex]
2. Use one of the points to find the y-intercept (b). Let's use (1, 2):
[tex]2 = \frac{13}{3} (1)+b[/tex]
[tex]2 = \frac{13}{3}+b[/tex]
To isolate b, subtract [tex]\frac{13}{3}[/tex] from both sides:
[tex]b= 2 - \frac{13}{3}[/tex]
[tex]b= \frac{6}{3} - \frac{13}{3}[/tex]
[tex]b = - \frac{7}{3}[/tex]
